PRC2 direct transfer from G-quadruplex RNA to dsDNA has implications for RNA-binding chromatin modifiers

Significance Studies of PRC2 in vitro indicate that RNA inhibits its histone methyltransferase (HMTase) activity through mutually antagonistic binding with nucleosomes, but some in vivo studies paradoxically suggest that RNA binding is necessary to facilitate its chromatin occupancy and HMTase activity. Our findings unveil a mechanism for direct exchange of RNA and DNA/nucleosome on the PRC2 protein complex, which reconciles these prior findings by allowing RNA regulation of PRC2 to be antagonistic or synergistic depending on RNA–nucleosome proximity. Furthermore, there is an increasing awareness that multiple chromatin-associated proteins exhibit regulatory RNA binding activity, and our findings indicate that this “direct transfer” mechanism may be generally required for RNA recruitment of proteins to chromatin.


Single-Molecule Dynamics Simulations:
Reactions (Supp. Fig. 11) were simulated and analyzed in R v4.1.1 with custom scripts (see Software, Data, and Materials Availability). Briefly, 'nucleosome' and 'protein' molecule coordinates were randomly scattered in a 3dimensional simulation box with periodic boundary conditions, 'RNA' molecule coordinates were added linearly to both sides of each nucleosome in intervals of twice the molecular diameter (2x pd), nucleosome and RNA coordinates were checked for molecular clash (proximity ≤ pd), and coordinate generation was repeated if necessary. Then, molecular diffusion was approximated by 'random walk' changes in coordinates at each time-step, and inter-molecular binding was defined at the end of each time-step as a proximity of pd or less between protein and nucleosome/RNA molecules. Molecules determined to be bound were set to a bound state, with their diffusion and additional binding capacity ablated, for a randomly sampled length of time based on the molecular pair's dissociation rate constant (k-1).
Specifically, [ET], [NT], RnN (RNA molecules per nucleosome), Kd, t (reaction time), τ (time-step), and ζ (dimensions of cubic simulation box) were user-provided, D (diffusion coefficient), pd (molecular diameter), and An (Avogadro's number) were established constants, and k1 and k-1 were calculated from other parameter values via Eq. 8.1-2. To generate initial conditions, numbers of nucleosome (Nn) and protein (En) molecules were calculated by rounding Eq. 8.3 to the nearest integers, numbers of RNA molecules (Rn) were calculated via Eq. 8.4, initial nucleosome and protein cartesian coordinates were sampled from a uniform distribution parameterized by [-ζ ÷2, ζ ÷2], RNA cartesian coordinates were calculated by 2x pd-interval additions and subtractions to the nucleosome x-coordinates, an intermolecular distance of 2x pd or greater was confirmed between all nucleosome and RNA molecules, and then coordinate assignment was repeated if necessary. To simulate diffusion between time-steps for each protein molecule in an unbound state, spherical coordinates for direction were sampled from a uniform distribution parameterized by [0, 2π], the spherical coordinate for magnitude was sampled from the Eq. 8.5 probability density function for random-walk diffusion, then spherical coordinates were converted to cartesian coordinates and added to the existing coordinate values. Molecules that diffused past a 'wall' in the defined simulation box during each time-step were moved a proportionate distance into the simulation box from the opposite 'wall' (periodic boundary conditions). To determine binding states after initial conditions and each diffusion step, the intermolecular distance to every protein molecule was calculated sequentially for every nucleosome/RNA molecule, the most proximal protein molecule with an intermolecular radius of pd or less was identified (if any), a binding state value of zero (unbound) was confirmed for the protein and nucleosome/RNA molecules, a residence time was sampled from an exponential distribution parameterized by k-1 and rounded to the corresponding integer number of time-steps, and the time-step number set as the new binding state value. Zero binding states indicate unbound molecules, non-zero binding states indicate bound molecules, and non-zero binding state values drop by 1 at the end of each time-step (after diffusion and binding state updates).

Equations:
For Eq. 1.1-10, rate constants are defined in Fig. 1 For Eq. 2, PE is polarization at equilibrium for a given [ET], Pmax is the maximum polarization, Pmin is the minimum polarization, [ET] is the total protein concentration, and Kd app is the apparent dissociation constant.
For Eq. 3.1-2, Nt is relative polarization at a given time (t), Nmin is the minimum relative polarization, λ is the decay rate constant, and koff obs is the observed dissociation rate.
For Eq. 5.1-11, terms are defined in Fig. 4a and Supp. Table 1, equations give rates of change for indicated reactants as a function of time (t), and bracketed terms indicate concentrations. For Eq. 6.1-13, terms are defined in Fig. 5a and Supp. Table 1, equations give rates of change for indicated reactants as a function of time (t), and bracketed terms indicate concentrations. For Eq. 7.1-5, apply Eq. 5 notation. For Eq. 7.5b, apply Eq. 6 notation.
(Eq. 7.1) For Eq. 8.1-8, P(r | D, τ) is the relative likelihood function of displacement (r) given a time-step interval (τ) and diffusion coefficient (D), Nn is the number of nucleosome molecules, An is Avogadro's number, [NT] is the total concentration of nucleosome, ζ is the dimension length of a cubic simulation box, Rn is the number of RNA molecules, Nn is the number of nucleosome molecules, RnN is the number of RNA molecules per nucleosome, BN/R is the fraction of nucleosome/RNA molecules bound by protein, N 1+ is the number of protein-bound nucleosome molecules, R 1+ is the number of protein-bound RNA molecules, PEN is protein-nucleosome proximity, N ; 222⃗ is the position of the i th nucleosome molecule, E ; < = 2222222⃗ is the position of the j th closest unbound protein molecule (to the i th nucleosome molecule), Mε is relative effective molarity, pd is molecular radius, Eζ 0 is the number of unbound protein molecules in the simulation box, and Ei 0 is the number of unbound protein molecules within a 10 x pd radius of the i th nucleosome molecule.

KdP
Equilibrium dissociation constant for protein-ligand interaction (Table 1) KdD Equilibrium dissociation constant for protein-competitor interaction k-1P Unimolecular rate constant for intrinsic protein-ligand dissociation (Fig. 1) k1P Bimolecular rate constant for association of protein and ligand (Fig. 1)

k-1D
Unimolecular rate constant for intrinsic protein-competitor dissociation (Fig. 1) k1D Bimolecular rate constant for association of protein and competitor (Fig. 1) kθP Bimolecular rate constant for protein direct transfer from competitor to ligand (Fig. 1) kθD Bimolecular rate constant for protein direct transfer from ligand to competitor (Fig. 1)

k-1N
Unimolecular rate constant for intrinsic protein-nucleosome dissociation  k1N Bimolecular rate constant for association of protein and nucleosome  k-1R Unimolecular rate constant for intrinsic protein-RNA dissociation  k1R Bimolecular rate constant for association of protein and RNA  kcat Unimolecular rate constant for methyltransferase catalysis  kθΝΝ Bimolecular rate constant for protein direct transfer from nucleosome to nucleosome (Fig. 4) kθΝ Bimolecular rate constant for protein direct transfer from RNA to nucleosome (Fig. 4) kθR Bimolecular rate constant for protein direct transfer from nucleosome to RNA (Fig. 4) α Tuning parameter for effective molarity of direct transfer reactions  β Tuning parameter for the effect of co-bound RNA on methyltransferase catalysis by proteinnucleosome-RNA complex (Fig. 5)

δ1N
Tuning parameter for the effect of pre-bound nucleosome on RNA association with protein-nucleosome complex (Fig. 5)

δ1R
Tuning parameter for the effect of co-bound RNA on methyltransferase catalysis (Fig. 5)

δ2N
Tuning parameter for the effect of co-bound RNA on nucleosome dissociation from proteinnucleosome-RNA complex (Fig. 5)

δ2R
Tuning parameter for the effect of co-bound nucleosome on RNA dissociation from proteinnucleosome-RNA complex (

EN
Protein bound to nucleosome  ER Protein bound to  EN m Protein bound to methylated nucleosome  ENR Protein bound to nucleosome and RNA (Fig. 5) EN m R Protein bound to methylated nucleosome and RNA (Fig. 5)